In [1]}, the authors proved that in the periodic channel steady solutions whose vorticity is sufficiently close to that of Couette in \(H^s\)  with \(s>3/2\)  must be shear. They also constructed non-shear steady solutions whose vorticity is arbitrarily close to the Couette flow vorticity in \(H^s\) , with \(s<3/2\) , implying that inviscid damping to a shear flow is not true in low regularity.
